MathPro Classification Scheme

• Algebra
  • Age problems
    - cryptarithm
    - digits
    - fathers and sons
    - primes
    - reciprocals of squares of ages
  • Algorithms
  • Ancestors
  • Calculators
  • Calendar problems
    - calendar cycles
    - day of week
    - days in month
    - digit problems
    - Friday the 13th
    - nonstandard calendars
    - significant dates
  • Clock problems
    - angle of hands
    - geometry
    - hands
    - meters
    - water clocks
  • Complex numbers
    - geometry of complex numbers
    - identities
    - inequalities
  • Continued fractions
    - arithmetic progressions
    - peridoic
    - periodic
    - radicals
    - solution of equations
  • Determinants
    - Bernoulli numbers
    - combinatorial properties
    - combinatorics
    - factorials
    - fractions
    - gamma function
    - Hankel matrices
    - integrals
    - polynomials
    - symmetric group
  • Discriminants
  • Elections
  • Exponential equations
  • Factorization
    - degree 2
    - degree 4
    - degree 5
    - degree 8
    - degree n
    - irreducible polynomials
  • Fair division
  • Finite differences
  • Finite products
  • Finite sums
    - binomial coefficients
    - factorials
    - fractions
    - harmonic series
    - logarithms
    - polynomials
  • Floor function
    - degree 3
    - finite sums
    - identities
    - inequalities
    - linear
    - radicals
    - solution of equations
  • Functional equations
    - 1 parameter
    - 2 parameters
    - derivatives
  • Functions
  • Gaussian polynomials
  • Geometry of zeroes
    - complex numbers
    - cubic
    - cubics
    - degree n
    - derivatives
    - determinants
  • Graphs
    - degree 4
    - equations
    - exponentials
    - parabolas
  • Identities
    - a+b+c=0
    - finite sums
    - multinomial coefficients
    - Pascal's triangle
    - powers
  • Inequalities
    - absolute value
    - binomial coefficients
    - degree 2
    - degree 3
    - degree 4
    - degree 6
    - equivalence
    - exponentials
    - finite products
    - finite sums
    - fractions
    - harmonic series
    - infinite sums
    - logarithms
    - polynomials
    - positive reals
    - powers
    - radicals
  • Interest problems
  • Iterated functions
  • Logarithms
  • Maxima and minima
    - combinations
    - constrained extrema
    - exponentials
    - finite products
    - finite sums
    - fractions
    - graphs
    - permutations
    - polynomials
    - radicals
  • Means
    - arithmetic mean
    - geometric mean
  • Measuring problems
  • Money problems
    - interchanged digits
    - multiply equals add
    - ratios
  • Numerical calculation
  • Partial fractions
  • Partitioned sequences
    - Fibonacci numbers
    - plus 1
    - plus 4
    - plus 6
  • Periodic sequences
  • Polynomial divisibility
    - complex numbers
    - degree 5
  • Polynomials
    - Bernstein polynomials
    - degree 3
    - degree 3n
    - factorization
    - fixed points
    - homogeneous
    - integer coefficients
    - largest coefficients
    - linear independence
    - number of terms
    - orthogonal polynomials
    - positive definite
    - properties
    - roots and coefficients
    - zeroes
  • Radicals
    - continued radicals
    - sum of cube roots
    - sum of square roots
  • Range
  • Rate problems
    - cars
    - drummers
    - maxima and minima
    - particles
    - planes
    - records
    - rowing
    - running
    - swimming
    - trains
    - trips
  • Recurrences
    - 2 by 2 non-linear difference systems
    - degree 3
    - difference equations
    - find a formula
    - fractions
    - sequences
  • Roots of unity
  • Sequences
    - find formula
    - functions
    - inequalities
    - odd and even
    - rational expressions
  • Sets
  • Solution of equations
    - absolute value
    - degree 2
    - degree 4
    - degree 5
    - degree 6
    - degree 7
    - exponential equations
    - fractions
    - logarithms
    - radicals
  • Sports
    - baseball
    - billiards
    - car racing
    - pool
  • Spring scale
  • Substitution
  • Sum of powers
    - degree 5
    - formulas
    - inequalities
    - polynomials
    - recurrences
    - roots
  • Systems of equations
    - 2 variables
    - 3 variables
    - 5 variables
    - 8 variables
    - equations over fields
    - logarithms
    - n variables
    - porisomatic equations
    - sum of powers
  • Theory of equations
    - constraints on roots
    - functions of roots
    - identities
    - location of zeroes
    - number of solutions
    - rational roots
    - real roots
    - roots
    - systems of equations
  • Undetermined coefficients
  • Uniform growth
    - grazing
    - provisions
    - snowplows
  • Units
  • Venn diagrams
  • Weights
    - balance scales
    - beam balance
    - innacurate balance
  • Word problems
    - area
    - expressions
    - math contests
    - passengers
    - percentage
    - races
    - sequences
  • Work problems
• Analysis
  • Arc length
  • Bessel functions
  • Bijections
  • Borel sets
  • Complex variables
    - analytic continuation
    - analytic function
    - analytic functions
    - Banach spaces
    - bijections
    - bounded functions
    - conformal mapping
    - finite sums
    - Fourier series
    - harmonic functions
    - inequalities
    - maxima and minima
    - number theory
    - rational functions
  • Convergence of sequences
    - complex l squared space
    - exponentials
    - finite sums
    - logarithms
    - recurrences
  • Convergence of series
    - convergence criteria
    - exponentials
    - factorials
    - functions
    - harmonic series
    - inequalities
    - logarithms
    - partial sums
    - polynomials
    - powers
    - primes
    - summability
    - tails
  • Cosine transform
  • Curves
    - barycentric coordinates
    - curve stitching
    - horizontal tangents
    - parametric curves
    - second derivatives
    - sketching
    - space curves
    - tangent-normals
    - tangents
    - transformations
  • Derivatives
    - chain rule
    - convex functions
    - decimal representation
    - finite sums
    - functions
    - Gateaux and Frechet derivatives
    - higher derivatives
    - inequalities
    - maxima and minima
    - monotone functions
    - one-sided derivatives
    - roots
  • Diffeomorphisms
  • Differential equations
    - domain of definition
    - initial value problems
    - order 2
    - order 3
    - order n
    - Riccati equation
    - separable equations
  • Folium of Descartes
  • Fourier series
  • Fractional parts
  • Functions
    - 3 variables
    - analytic
    - composition of functions
    - continuous functions
    - convex functions
    - differentiable functions
    - entire functions
    - graphs
    - infinite series
    - linear
    - meromorphic functions
    - monotone functions
    - periodic
    - polynomials
    - real-valued functions
    - uniform continuity
  • Gamma function
  • Hypergeometric functions
    - differential-recurrence relations
    - evaluations
    - gamma function
    - positive integers
    - transformations
  • Inequalities
    - centroids
    - infinite sums
    - point moving in a square
  • Infinite products
  • Infinite sums
    - binomial coefficients
    - doubly infinite series
    - exponentials
    - factorials
    - floor function
    - fractions
    - integrals
    - multinomial coefficients
    - nearest neighbor
    - radicals
  • Integral inequalities
    - definite integrals
    - derivatives
    - improper integrals
    - improper Riemann integrals
  • Integrals
    - area
    - binomial coefficients
    - Claussen's integral
    - differentiability
    - double integrals
    - evaluations
    - finite products
    - finite sums
    - fractional integrals
    - functions
    - gamma function
    - improper double integrals
    - improper integrals
    - maxima and minima
    - multiple integrals
    - principal value
    - triple integrals
  • Laplace transforms
  • Legendre polynomials
  • Limits
    - binomial coefficients
    - exponentials
    - factorials
    - finite products
    - finite sums
    - floor function
    - functions
    - inequalities
    - infinite products
    - infinite sums
    - iterated functions
    - logarithms
    - nearest integer
    - normed spaces
    - number theory
    - radicals
    - recurrences
    - sequences
    - sum of powers
    - sum of products
    - trigonometry
  • Location of zeroes
    - complex variables
    - determinants
    - exponential equations
    - exponentials
    - orthogonal polynomials
    - polynomials
  • Maclaurin series
  • Maxima and minima
    - geometry
    - polynomials
    - trigonometric series
  • Measure theory
    - almost everywhere linear functions
    - arcs
    - Borel sets
    - Cantor-Lebesgue function
    - computational complexity
    - finitely-additive measures
    - finitely additive measures
    - harmonic analysis
    - homeomorphisms
    - integrals
    - Lebesgue integrals
    - measurable functions
    - polynomials
    - residual subsets
    - unit circle
  • Partial derivatives
  • Power series
    - coefficients
    - factorials
    - integrals
  • Properties of functions
  • Pursuit problems
    - circles
    - pigs
    - rabbits
    - ships
  • Rate problems
  • Riemann zeta function
    - inequalities
    - infinite sums
    - limits
  • Sequences
    - density
    - infinite matrices
    - infinite series
    - iterated functions
    - limit point
    - limits
    - logarithmic convexity
    - pairs of sequences
    - power series
  • Systems of differential equations
    - 2x2 homogeneous systems
    - 2x2 non-linear systems of ODE's
    - 2x2 systems of non-linear ordinary differential equations
    - 2x2 systems of ordinary differential equations
    - 3x3
    - degree 2
    - nxn
  • Theta series
• Applied Mathematics
  • Airplanes
  • Astronomy
  • Computer science
  • Electrical networks
  • Physics
    - buoyancy
    - cogwheels
    - equations of motion
    - knots
    - masses
    - moving particles
    - particles
    - pendulums
    - rods
    - rolling particles
    - rotation
• Combinatorics
  • Arrays
    - array operations
    - Bingo
    - hexagons
    - nim
    - paths
    - positive and negative
    - rank
    - symbols in squares
  • Ballots
  • Card shuffling
  • Coloring problems
    - circles
    - intervals
    - points in a square
    - points in plane
    - points in space
    - points on a circle
    - prisms
    - triangles
  • Compositions
  • Computational complexity
  • Configurations
    - collections of objects
    - collinear points
    - committees
    - couples
    - docking
    - groups of people
    - Latin rectangles
    - Latin squares
    - leagues
    - maxima and minima
    - v-k-lambda
  • Counting problems
    - average value
    - billiards
    - cards
    - combinations
    - inversions
    - parenthesization
    - paths
    - Scrabble
    - sequences
    - stacking of balls
    - subsets
    - targets
  • Dice problems
  • Digit problems
    - binary numbers
    - consecutive digits
    - distinct digits
    - increasing or decreasing
    - normal integers
    - page numbers
    - partitions
    - permutations
    - product of digits
  • Elevators
  • Geometry
    - circles
    - configurations
    - distances
    - hexagons
    - Hilbert space
    - lines in a plane
    - n-dimensional geometry
    - partitions
    - pentagons
    - points in plane
    - points in space
    - polygons
    - tetrahedra
    - toothpicks
  • Graph theory
    - arrays
    - directed walks
    - distance
    - Eulerian circuits
    - Hamiltonian circuits
    - infinite tree
    - matchings
    - matrices
    - networks
    - Petersen graph
    - planar graphs
    - properties
    - reconstruction
    - subgraphs
    - vertex degrees
  • Lattice paths
  • Lattice points
  • Letters and envelopes
  • Locks and keys
  • Measuring problems
  • Money problems
    - coin tossing
    - maxima and minima
    - stamps
  • Mutual acquaintances
    - 10 people
    - 5 people
    - 6 people
    - circular table
    - groups of 4 people
    - hand shakes
  • Pascal's triangle
  • Paths
  • Permutations
    - cycles
    - digits
    - fixed points
    - products of transpositions
    - rises
    - sorting
    - up-down permutations
    - vector products
  • Points on circle
  • Polygon counting
    - equilateral triangles
    - parallelograms
    - rectangles
    - squares
    - triangles
  • Prisoners
  • Seating arrangements
  • Sequences
  • Series
  • Sets of numbers
    - closure properties
    - counting problems
    - odd and even
    - Ramsey Theory
    - sums
  • Sorting
  • Substitution codes
  • Switches
  • Tournaments
    - algorithms
    - chess tournaments
    - incidence matrices
    - tennis
  • Word formation
    - counting problems
    - good arrangements
• Cryptarithms
  • Alphametics
    - animals
    - base conversions
    - cards
    - chemical equations
    - chess moves
    - Christmas
    - colors
    - congruences
    - constructions
    - crossword puzzle
    - division
    - doubly true
    - elements
    - equations
    - Etruscan
    - factorials
    - fish
    - floor function
    - food
    - formulas
    - German
    - Hebrew
    - indefinite sums
    - Japanese
    - measures
    - money
    - multiplication
    - names
    - numbers
    - phrases
    - places
    - planets
    - Polish
    - Pythagorean alphametics
    - radicals
    - simultaneous alphametics
    - squares
    - states
    - story problems
    - words
  • Digimetics
  • Encrypted messages
    - encrypted date
    - geometry
  • Integrals
  • Multiplication
  • Powers
  • Prime factorization
  • Repeating decimals
  • Simultaneous cryptarithms
  • Skeletons
    - division
    - multiplication
    - square roots
  • Word squares
    - squares
• Geometry
  • Affine transformations
  • Analytic geometry
    - area
    - centroids
    - circles
    - conics
    - distance
    - family of lines
    - locus
    - maxima and minima
    - parametric equations
    - polar curves
    - symmetry
  • Angle measures
    - circles
    - slope
  • Annulus
    - area
    - covering problems
    - rectangles
  • Arbelos
  • Butterfly problem
  • Cake cutting
  • Chain of circles
    - tangent circles
  • Characterizations
    - circles
    - concurrence
    - equilateral triangle
    - limiting figures
    - semicircles
    - star of David
    - triangles
  • Circles
    - angles
    - arcs
    - area
    - chords
    - concurrent circles
    - mixtilinear triangles
    - orthogonal circles
    - two circles
  • Combinatorial geometry
    - circles
    - lines in a plane
    - regions
    - triangulations
  • Conics
    - conjugates
    - constructions
    - hexagon
    - hyperbolas
    - projective geometry
    - quadratic relations
  • Constructibility
  • Constructions
    - angles
    - chords
    - circles
    - conics
    - equilateral triangles
    - lines
    - points
    - rulers
    - squares
    - straightedge only
    - triangles
  • Convexity
    - balls
    - buoyancy
    - corners
    - diameters
    - inequalities
    - ovals
    - points of symmetry
    - radius of curvature
    - Steiner symmetrizations
  • Covering problems
    - covering a square
    - covering a triangle
    - covering of points
    - perimeter
  • Cyclic quadrilaterals
    - angle bisectors
    - n-dimensional geometry
    - parallelograms
    - perpendiculars
    - ratios
  • Differential geometry
  • Dissection problems
    - circles
    - isosceles triangles
    - polygons
    - quadrilaterals
    - rectangles
    - rhombuses
    - right triangles
    - squares
    - triangles
  • Ellipses
    - area
    - chords
    - focal radii
    - inscribed in kite
    - inscribed in rhombus
    - inscribed in triangle
    - maxima and minima
    - parabolas
    - regions
    - tangent ellipses
  • Envelopes
  • Equilateral triangles
    - altitudes
    - area
    - centroids
    - circles
    - circumcircle
    - concentric triangles
    - hexagons
    - interior point
    - maxima and minima
    - orthogonal projection
    - reflections
    - right triangles
    - semicircles
    - squares
  • Fallacies
  • Family of lines
  • Grazing goat
  • Hexagons
    - circles
    - closure theorems
    - conic sections
    - convex hexagons
    - equiangular
    - equilateral triangles
    - opposite sides parallel
  • Inequalities
    - altitudes
    - area
    - circumcircle
    - medians
    - parallelograms
    - point in triangle
    - points in plane
    - polygons
    - quadrilaterals
    - radii
    - trapezoids
    - triangles
  • Isoperimetric inequalities
    - area
    - polygons
    - squares
  • Isosceles right triangles
  • Ladders
  • Lattice points
    - area
    - center of gravity
    - centroids
    - collinear points
    - discs
    - distances
    - mappings
    - midpoints
    - spirals
    - taxicab metric
  • Lattice polygons
    - equilateraltriangles
    - lattice polyhedra
    - lattice triangles
    - regular pentagons
    - right triangles
    - squares
    - triangles
  • Lehmus's Theorem
  • Limiting figures
    - chain of circles and polygons
    - circles
    - incribed triangles and circles
    - polygons
    - quadrilaterals
    - right triangles
    - triangles
  • Locus
    - angles
    - area
    - circles
    - conics
    - ellipses
    - equilateral triangles
    - hyperbolas
    - hyperboloids
    - linkages
    - parabolas
    - parallel lines
    - right triangles
    - squares
    - triangles
    - trigonometry
  • Malfatti circles
  • Map problems
  • Maxima and minima
    - area
    - circular arcs
    - compact subsets of the plane
    - corridors
    - curves
    - excircles
    - incircle
    - isosceles triangles
    - rectangles
    - right triangles
    - shortest paths
    - solid geometry
    - triangles
  • N-dimensional geometry
    - combinatorial geometry
    - cubes
    - distances
    - n-cube
    - rectangular parallelepiped
    - regular simplex
    - simplex
    - unit ball
    - volume
    - width
  • Non-Euclidean geometry
  • Packing problems
  • Paper folding
    - circles
    - cubes
    - equilateral triangles
    - octahedron
    - regular tetrahedron
    - tetrahedrons
  • Parabolas
    - circles
    - derivatives
    - normals
    - tangents
  • Parallelograms
    - area
    - convex quadrilaterals
    - directly similar triangles
    - midpoint property
    - right triangles
  • Pentagons
  • Pigeonhole
    - annulus
    - circles
    - equilateral triangles
    - regular hexagons
  • Points in plane
  • Polygons
    - equilateral
    - hexagons
    - reflex angles
    - sum of diagonals
  • Projective geometry
    - 5th dimension
    - cross ratio
    - homogeneous coordinates
    - photographs
    - projective 3-space
    - straight lines
    - triangles
  • Quadrilaterals
    - area
    - centroid
    - circles
    - circumscribed
    - erected figures
    - inscribed and circumscribed
    - maxima and minima
    - perpendicular diagonals
    - perpendicular lines
  • Rectangles
    - circles
    - equilateral triangles
    - golden rectangle
    - inscribed
    - triangles
  • Regular dodecagons
  • Regular heptagons
  • Regular hexagons
  • Regular octagons
  • Regular pentagons
  • Regular polygons
    - angles
    - area
    - inequalities
    - infinite products
    - inscribed polygon
    - interior point
    - limits
    - maxima and minima
    - rigidity
    - sum of segments
  • Right triangles
    - altitudes
    - circular arcs
    - erected figures
    - incircle
    - interior points
    - length of sides
    - perimeter
    - perpendiculars
    - radii
    - rectangles
    - similar triangles
    - square on hypotenuse
  • Rolling
  • Rusty compass
  • Semicircles
  • Similarity
    - cevians
    - directly similar
    - triangles
  • Squares
    - areas
    - circles
    - determination of angles
    - inscribed in triangle
    - interior line segments
    - interior point
    - lengths
    - paths
    - right triangles
  • Sylvester's Theorem
  • Tessellations
    - Chinese checkerboard
    - equilateral triangles
    - hexagons
    - rectangles
    - squares
  • Tiling
  • Trapezoids
    - areas
    - cyclic
    - harmonic range
    - sides
  • Triangle inequalities
    - altitudes
    - altitudes and medians
    - angle bisectors
    - angle bisectors and medians
    - angle bisectors extended
    - angles
    - angles and radii
    - angles and sides
    - Brocard angle
    - circumradii extended
    - interior points
    - medians and sides
    - medians extended
    - point in space
    - radii
    - radii and sides
    - sides
    - sides and area
    - two triangles
  • Triangles
    - 120 degree angle
    - altitudes
    - angle bisectors
    - area
    - Brocard angles
    - centers
    - centroids
    - cevial triangles
    - cevians
    - circles
    - circumcircles
    - equal areas
    - erected figures
    - excircles
    - exradii
    - incenter
    - inscribed circles
    - inscribed squares
    - inscribed triangle
    - interior point
    - isosceles triangles
    - length
    - limits
    - medial triangle
    - medians
    - orthocenter
    - relations among parts
    - special types
    - symmedians
    - transformations
  • Vectors
• Higher Algebra
  • Binary operations
    - number theory
    - polynomials over fields
  • Fields
  • Galois theory
  • Groups
    - affine motion
    - alternating and symmetric groups
    - alternating group
    - center by finite groups
    - character theory
    - commutativity conditions
    - complex numbers
    - finite groups
    - groups of isometries
    - homomorphisms
    - isomorphisms
    - normal subgroups
    - permutation groups
    - sets
    - simple non-abelian groups
    - subgroups
    - triangles
  • Lattices
  • Rings
    - associative ring
    - commutative rings
    - division rings
    - divisors of zero
    - endomorphisms
    - equations
    - group of units
    - ideals
    - lattices
    - linear algebra
    - modules over commutative rings
    - partial ordering
    - R-modules
    - squares
  • Semigroups
• Linear Algebra
  • Determinants
    - limits
    - maxima and minima
    - partitioned matrices
    - singular
    - submatrices
  • Eigenvalues
    - commuting matrices
    - complex numbers
    - Gram matrix
    - Hermitian matrices
    - pairs of matrices
    - polynomials
    - real tri-diagonal matrices
  • Eigenvectors
  • Gram-Schmidt process
  • Hilbert spaces
  • Linear transformations
  • Maps
  • Matrices
    - 0-1 matrices
    - adjoints
    - column vectors
    - Hermitian
    - inequalities
    - inverses
    - orthogonal
    - Perron roots
    - positive definite
    - positive semidefinite
    - reflection
    - skew symmetric
    - stochastic matrices
    - submatrices
    - symmetric
    - triangular
    - Vandermonde
  • Matrix equations
  • Matrix sequences
  • Minimal polynomials
  • Normed spaces
  • Permanents
  • Rank
    - matrices
    - nonsingular matrix
  • Trace
  • Vector spaces
• Number Theory
  • Abundant numbers
  • Additive number theory
  • Algebraic number theory
  • Algorithms
  • Amicable numbers
  • Arithmetic operations
  • Arithmetic progressions
    - 1983
    - cubes
    - powers
    - primes
    - squares
    - sum of squares
    - ternary representation
    - triangular numbers
  • Arrays
    - 3 by 3
    - cubical array
    - divisibility
    - finite sums
    - hexagons
    - infinite arrays
    - multiples
    - n by n
    - nine non-zero digits
    - numbers in an array
    - pandigital numbers
    - pentagons
    - primes
    - relatively prime integers
    - sum of products
    - sum of series
  • Base systems
    - base 2
    - digit reversals
    - divisibility
    - factorials
    - hexagonal numbers
    - logic
    - maxima and minima
    - negative base systems
    - palindromes
    - parity
    - permutations
    - primes
    - repdigits
    - squares
    - terminal digits
  • Beatty's Theorem
  • Bernoulli numbers
  • Binomial coefficients
    - analysis
    - combinatorics
    - congruences
    - consecutive
    - divisibility
    - finite sums
    - inequalites
    - odd and even
    - powers
    - primes
    - remainders
  • Collatz problem
    - insomniac numbers
    - sequences
  • Composite numbers
  • Congruences
    - binomial coefficients
    - coprime integers
    - divisors
    - Euler numbers
    - exponential
    - Fermat
    - primes
    - quadratic
    - recurrences
    - triangular numbers
  • Continued fractions
  • Cubes
  • Decimal representation
    - approximations
    - automorphic numbers
    - digit problems
    - digit sums
    - period
    - periods
    - recursion equations
    - sequences of squares
  • Dedekind's function
  • Deficient numbers
  • Dense sets
  • Difference equations
    - congruences
    - exponentials
    - Fibonacci numbers
    - nth differences
    - second order
  • Digit problems
    - base conversion
    - cancelled digits
    - consecutive digits
    - cubes
    - cyclic shift
    - cyclically consecutive
    - deleted digit
    - distinct digits
    - divisibility
    - inequalities
    - interchanged digits
    - juxtapositions
    - maxima and minima
    - missing digits
    - multiples
    - multiplicative digital root
    - numerical evaluation
    - partitions
    - permutations
    - powers
    - primes
    - product of consecutive integers
    - pronic numbers
    - reversals
    - squares
    - sum of cubes of digits
    - sum of digits
    - sum of squares of digits
    - terminal digits
  • Diophantine equations
    - degree 11
    - degree 2
    - degree 3
    - degree 4
    - degree 5
    - degree 8
    - exponential equations
    - factorials
    - Fermat's Problem
    - Fibonacci numbers
    - linear equations
    - primes
    - radicals
    - solution in primes
    - solution in rationals
    - systems of equations
  • Diophantine representation
  • Divisibility
    - binomials
    - consecutive divisors
    - consecutive integers
    - exponentials
    - factorials
    - finite products
    - finite sums
    - infinite sums
    - polynomials
    - primes
    - remainders
  • Divisors
    - 1981
    - finite sums
    - number of divisors
    - powers of 2
    - product of divisors
    - quadratic forms
  • Equations
  • Euler totient
    - composite numbers
    - congruences
    - Dirichlet set
    - divisibility
    - finite series
    - finite sums
    - inequalities
    - limits
    - modulo arithmetic
    - primes
    - series
    - summation
  • Factorials
    - factorization
    - fractions
    - inequalities
    - pandigital numbers
    - prime factorization
    - squares
    - summation of series
    - terminal digits
    - terminal zeroes
  • Farey sequences
  • Fermat numbers
  • Fibonacci and Lucas numbers
    - arithmetic means
    - congruences
    - divisibility
    - finite sums
    - forms
    - geometry
    - identities
    - probability
    - progressions
  • Fibonacci numbers
    - congruences
    - covering problems
    - factors
    - finite sums
    - forms
    - geometry
    - greatest common divisor
    - identities
    - infinite products
    - infinite sums
    - properties
  • Floor function
    - absolute values
    - cube roots
    - Euler totient
    - finite sums
    - forms of numbers
    - golden ratio
    - identities
    - number of solutions
    - odd and even
    - sequences
    - square roots
    - summation
  • Forms of numbers
    - Boneh numbers
    - congruences
    - difference of two squares
    - exponentials
    - finite series
    - primes
    - rational numbers
    - squares
  • Fractional parts
    - exponential equations
    - powers
    - primes
    - sqrt 5
  • Gaussian sums
  • Generating functions
  • Geometry
    - area
    - chessboards
    - dissection
    - divisibility
    - hexagons
    - integral distances
    - Plutarch
    - pyramids
    - rectangles
    - rectangular parallelepipeds
    - right triangles
    - semicircles
    - squares
    - tetrahedra
    - triangles
  • Goldbach's conjecture
  • Greatest common divisor
  • Harmonic series
  • Heronian triangles
  • Higher order recurrences
  • Inequalities
    - absolute value
    - divisibility
    - exponential
    - fractional negative exponents
    - multiples
    - products
    - rational expressions
    - sum of series
  • Integer-valued polynomials
  • Least common multiple
    - committees
    - ordered quadruples
    - series
  • Legendre symbol
    - finite sums
    - primes
    - quadratic reciprocity
  • Lucas numbers
    - congruences
    - divisibility
    - divisibility properties
    - forms
    - geometry
    - identities
    - polynomial divisibility
    - right triangles
    - ring of integers modulo n
    - trigonometry
  • Maxima and minima
    - distances
    - divisibility
    - partitions
    - powers
    - products
    - radicals
    - sum of two squares
  • Mersenne numbers
  • Modular arithmetic
    - factorials
    - infinite sums
    - iterated exponentials
    - Legendre symbol
    - odd integers
    - sum of series
  • Moebius function
  • Monotone functions
  • Multigrades
  • Multiplicative functions
  • Normal numbers
  • Number representations
    - cubes
    - powers of 2
    - simplification of radicals
    - sum of fourth powers
  • Palindromes
    - base systems
    - concatenation of squares
    - infinite sums
    - pandigital numbers
    - prime factors
    - primes
    - products
    - squares
  • Pandigital numbers
    - divisibility
    - maxima and minima
    - multiples
    - palindromes
    - persistent numbers
    - power of prime
    - powers
    - primes
    - square and cube roots starting pandigitally
    - square roots
    - squares
  • Partitions
    - inequalities
    - maxima and minima
    - maximum product
    - partitions of 12
    - perfect partitions
    - sum of elements
  • Pascal's triangle
  • Pell numbers
  • Perfect numbers
  • Permutations
    - matrices
    - maxima and minima
    - multipliers
    - power loops
    - products
  • Polygonal numbers
    - binomial coefficients
    - hexagons
    - nonagonal numbers
    - tetrahedral numbers
  • Polynomial congruences
  • Polynomials
    - 5th degree
    - binomial coefficients
    - complex numbers
    - Diophantine equations
    - divisibility
    - exponential
    - Galois theory
    - primes
    - quadratics
    - rational functions
    - second degree
    - set theory
    - theory of equations
  • Powerful numbers
  • Powers
    - binomial coefficients
    - rational exponents
    - roots
    - squares
    - temperature scales
  • Powers of 2
  • Primes
    - analytic number theory
    - arithmetic progressions
    - determinants
    - digit reversals
    - digits in descending order
    - divisibility
    - forms of numbers
    - gaps
    - inequalities
    - intervals
    - partitions
    - polynomials
    - powers
    - prime circles
    - product of primes
    - sequences
    - sum of primes
  • Primitive roots
  • Pronic numbers
  • Pythagorean triples
    - angles
    - area
    - digit reversals
    - divisibility
    - generators
    - given hypotenuse
    - given perimeter
    - given side
    - hypotenuse
    - inradius
    - maxima and minima
    - pandigital numbers
    - perimeters
    - product of sides
  • Quadratic fields
  • Quadratic residues
  • Rational expressions
    - divisibility
    - exponents
    - finite products
    - finite sums
    - inequalities
    - real number line
  • Recurrences
    - determinants
    - divisibility
    - Fibonacci and Lucas numbers
    - Fibonacci numbers
    - generalized Fibonacci sequence
    - higher order linear recurrences
    - inequalities
    - Lucas numbers
    - maxima and minima
    - number representations
    - Pell equation
    - perfect numbers
    - second order linear
  • Repdigits
  • Repunits
    - algorithms
    - composite numbers
    - Mersenne primes
    - squares
    - twin primes
  • Schnirelmann density
  • Sequences
    - density
    - finite sequences
    - harmonic mean
    - law of formation
    - maxima and minima
    - monotone sequences
    - sequences of digits
  • Series
    - binomial coefficients
    - congruences
    - digit problems
    - factorials
    - finite series
    - fractions
    - inequalities
    - powers
    - primes
  • Sets
    - arithmetic mean
    - divisibility
    - geometric means
    - powers of 2
    - primes
    - sum of elements
  • Sets with same sum
    - odd numbers
    - polynomials
    - sets with same product
    - squares
  • Squares
    - difference of two squares
    - divisibility
    - juxtaposition
    - powers of 2
    - Pythagorean triples
    - sequences
    - subadditivity
    - sum of digits
    - sum of squares
  • Sum of divisors
    - numerical functions
    - prime factors
    - primes
  • Sum of powers
  • Sum of squares
    - 1984
    - consecutive squares
    - divisibility
    - identical digits
    - polynomials
    - primes
    - squares
  • Sum of two squares
  • Systems of congruences
  • Triangles
    - altitudes
    - area
    - areas
    - ciarcles
    - cot
    - numbers on vertices
    - obtuse triangles
    - right triangles
  • Triangular numbers
    - base 9
    - digit problems
    - finite sums
    - primes
    - squares
  • Twin primes
  • Unit fractions
    - density
    - prime divisors
    - primes
  • Word problems
    - age problems
    - balance scale
    - hunters
    - multiples
• Probability
  • Broken rods
  • Bus routes
  • Cards
    - poker
  • Chess tournaments
  • Chessboard problems
  • Coin tossing
    - expectation
    - jury decisions
  • Continuous probability
  • Derangements
  • Dice problems
    - expected value
    - loaded dice
    - polyhedral dice
  • Digit problems
  • Discrete probability
    - bandits
    - committees
    - drawers
    - elections
    - flags
    - Hamming codes
    - horse racing
    - independent trials
    - jumping
    - lattice points
    - pies
    - rounding
    - switches
    - wives
    - word problems
  • Distributions
  • Duels
  • Expected value
    - coin tossing
    - maxima and minima
    - ordered partitions
    - random variables
    - sequences of random variables
    - socks
    - timers
    - urns
  • Game theory
    - archery
    - tennis
    - tournaments
  • Geometry
    - circles
    - continuous probability
    - cubes
    - equilateral triangular prisms
    - golf
    - points in circle
    - points on a line
    - points on sphere
    - triangles
  • Inequalities
  • Money problems
  • Number theory
  • Poisson distribution
  • Prisoners
  • Random variables
  • Repeated trials
  • Searching
  • Seating of couples
  • Sports
    - baseball
    - basketball
    - tennis
  • Theory of equations
  • Urns
    - limits
    - marbles
  • Walks
  • Warfare
• Recreational Mathematics
  • Anagrams
  • Block puzzles
  • Chess problems
    - created pieces
    - minimal moves to reach position
    - nonstandard playing conditions
    - probability
    - square control
    - tasks
  • Chess tours
    - area
    - bishop's tour
    - black king tour
    - closed archer's tour
    - knight's circuit
    - knight's tour
    - rooks tour
    - x-tour
  • Chessboard problems
    - coloring problems
    - coloring squares
    - deletion of squares
    - numbering of squares
  • Connecting dots
  • Crossnumber puzzles
  • Diagramless puzzles
  • Fair division
  • Game theory
    - chossing numbers
    - maxima and minima
    - number theory
    - probability
  • Games
    - backgammon
    - billiards
    - bridge
    - Monopoly
    - Nim
    - one to three
    - peg-solitaire
    - Snakes and Pits
    - surround
    - tic-tac-toe
    - tower of Hanoi
    - Yashima
    - Yellow Pigs
  • Logic puzzles
    - Caliban problems
    - incomplete information
    - liars and truthtellers
    - missionaries
    - relationships
    - secret messages
    - truth statements
  • Magic configurations
    - antimagic squares
    - gnomon magic squares
    - magic cubes
    - magic hexagons
    - magic octagons
    - magic squares
    - magic stars
    - toruses
  • Polyominoes
    - checkerboards
    - octominoes
    - pentominoes
    - rectangles
  • Solitaire games
  • Tangram puzzles
  • Tiling
    - covering problems
    - geometry
    - heptominoes
    - hexominoes
    - pentominoes
• Set Theory
  • Axiomatic set theory
  • Cantor set
  • Intervals
  • Mappings
  • Posets
  • Power set
  • Subsets
    - countable sets
    - intersection properties
    - symmetric difference
• Solid Geometry
  • Analytic geometry
    - ellipsoids
    - locus
    - parametric curves
    - regions
    - spheres
    - system of inequalities
    - tetrahedron
  • Constructions
  • Cubes
    - angle measures
    - coloring problems
    - diagonals
    - partitioning of vertices
    - partitions
    - rectangular solids
    - spherical geometry
    - volume
  • Cylinders
  • Dissection problems
  • Hyperboloids
  • Locus
    - planes
    - pyramids
    - quadratic surfaces
    - tetrahedra
  • Maxima and minima
  • Paper folding
  • Paraboloids
  • Pentahedra
  • Prisms
  • Pyramids
  • Rectangular parallelepipeds
  • Regular tetrahedra
    - integer distances
    - isoperimetric inequalities
    - maxima and minima
    - perpendicular distances
    - reflections
    - regular bodies
  • Right circular cones
    - ellipses
    - maxima and minima
    - plane sections
    - surface area
  • Skew polyhedra
  • Skew quadrilaterals
  • Solid angles
  • Space curves
  • Spheres
    - analytic geometry
    - area
    - boxes
    - inscribed regular solids
    - interior points
    - radii
    - tangent spheres
    - tangents
  • Spherical geometry
    - paths on Earth
    - spherical triangles
  • Tetrahedra
    - altitudes
    - area of faces
    - caltrops
    - centroids
    - co-spherical
    - even number of points
    - inscribed spheres
    - planes
    - radii
    - solid angles
    - volumes
  • Tetrahelix
  • Torus
• Statistics
  • Average deviation
  • Bernoulli trials
  • Means
  • Variance
• Symbolic Logic
  • Predicate calculus
• Topology
  • Connected components
  • Connectivity
  • Density criteria
  • Hilbert space
  • Homeomorphisms
  • Metric spaces
  • Product spaces
  • Second countability
  • Subspaces
  • T1 spaces
• Trigonometry
  • Approximations
  • Determinants
  • Elimination
  • Finite products
  • Finite sums
    - cos
    - csc
    - csc and cot
    - infinite sums
    - sec
    - sin
    - sin and cos
    - tan
  • Fourier series
  • Identities
    - arcsin
    - cot
    - finite products
    - sin
    - system
    - systems of equations
    - two variables
  • Inequalities
    - 2 variables
    - absolute value
    - cos
    - degree 4
    - finite sums
    - radicals
    - sin
    - tan
    - tanh
  • Infinite sums
  • Inradii
  • Maxima and minima
  • Numerical evaluation
    - sin
    - tan
  • Numerical identities
  • Quadrilaterals
  • Radian measure
  • Rational values
  • Solution of equations
    - cos
    - exact value
    - exponentials
    - inverse functions
    - powers
    - sin and cos
    - tan
    - transcendental equations
  • Solution of inequalities
  • Solution of triangles
  • Theory of equations
  • Triangles

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Last modified January 31, 1995.